On some of Ramanujanʹs Schläfli-type “mixed” modular equations Original Research Article

We give elementary proofs of seven Schläfli-type “mixed” modular equations recorded by Ramanujan on p. 86 of his first notebook. Previously, these equations were proved by Berndt by using the theory of modular forms. In the process, we also found three new Schläfli-type mixed modular equations of the same nature.